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Tsinghua University

光学

Tsinghua University via XuetangX

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Overview

作为理科专业基础课程，内容为经典光学，着重在波动性（电磁波），深入讨论波的性质，独立看深刻揭示光的波形，整体看为了后续量子力学进行必要铺垫。

从光是电磁波开始，介绍Maxwell方程导出电磁波以及其一般性质；再分别讨论下列重要物理现象：光在介质中的传播；几何光学简介；波的叠加而由此产生的重要的光的干涉，衍射和偏振等重要概念与现象以及它们的应用。

教学上突出对物理概念，物理图像的阐释与理解，对基本原理深入地讨论，再辅以严格的数学推导。

The course is about classical optics, focusing on the wave property of light. With such thorough discussion, we not only reveal important properties of light, but also offer a solid background for further study of quantum mechanics. The content of Optics will include:

1． What is ‘light’

2． Maxwell equations

3． Propagation of light in isotropic media

4． Geometric Optics

5． Superposition of waves

6． Interference

7. Diffraction

8. Polarization of light

Syllabus

  • Chapter 1 General Property of Wave(波的一般性质)
    • 1.0 History of Optics 光学的历史发展
    • 1.1 Why Classical Wave Theory is Correct 经典理论为何正确
    • 1.2 Wave and Wave Equation 波和波动方程
    • 1.3 Harmonic Wave 简谐波
    • 1.4 Phase Velocity and Phase Difference 相速度与相位差
    • 1.5 Superposition Principle 叠加原理
    • 1.6 Example of Superposition and Reciprocal Relation 叠加例子与反比关系
    • 1.7 Euler Formula and Phasor 波的复数表达和旋转矢量表示
    • 1.8 Doppler Effect 多普勒效应
    • 1.9 Doppler Broadening 多普勒展宽
    • 1.10 Plane Wave and Spherical Wave 平面波与球面波
    • 第一章习题
  • Chapter 2 Electro-Magnetic Wave(电磁波)
    • 2.1 Maxwell Equations(Maxwell 方程组)
    • 2.2 Wave Equation for E-M Field(电磁场的波动方程)
    • 2.3.1 Index of Refraction(折射率)
    • 2.3.2 Understanding n from Dipoles(用偶极模型理解折射率)
    • 2.4 E-M Wave is Transverse(电磁波是横波)
    • 2.5 Energy Flow of E-M Wave(电磁波的能流)
    • 2.6 Momentum and photo-Pressure(动量和光压)
    • 2.7.1 Dipole Oscillator 1(偶极振子1)
    • 2.7.2 Dipole Oscillator 2(偶极振子2)
    • 2.8 Radiation by Dipole Oscillator(偶极振子的辐射)
    • 第二章习题
  • Chapter 3 Light Propagation through Homogeneous and Isotropic Media
    • 3.1 Reflection and Refraction (反射与折射)
    • 3.2 Huygens Principle（惠更斯原理）
    • 3.3.1 Fermat Principle part1: Optical Path Length (费马原理第一部分：光程)
    • 3.3.2 Fermat Principle part2: an Explanation (费马原理第二部分：一种解释)
    • 3.4.1 Scattering Point of View 1 (散射图像1)
    • 3.4.2 Scattering Point of View 2 (散射图像2)
    • 3.5 Reflection and Refraction Rules Derived from Boundary Conditions of Maxwell Equations(利用Maxwell方
    • 3.6.1 The Basic problem and Setup of Coordinates (基本问题和坐标系的建立)
    • 3.6.2 The Reflection and Transmission Coefficients (发射与透射系数)
    • 3.6.3 Discussion on Amplitude of the Coefficients (对系数大小的讨论)
    • 3.6.4 Discussion on Phase of the Coefficients (对系数位相的讨论)
    • 3.7 Stokes Relation and Half Wavelength Difference (Stokes关系式和半波损)
    • 第三章习题
  • Chapter 4 Geometric optics(几何光学)
    • 4.1 Introduction(几何光学介绍)
    • 4.2 Important Jargons(重要的术语)
    • 4.3.1 Image formation by Spherical Surface and Paraxial Approxiamation(球面成像和傍轴近似)
    • 4.3.2 Image Formation Formula(成像公式)
    • 4.3.3 Example and Transverse Magnification(例题和横向放大率)
    • 4.4 Thin Lens(薄透镜)
    • 4.5 Thick Lens(厚透镜)
    • 4.6.1 Matrix Treatment 1: Matrix for Propagation and Refraction(矩阵处理1：表示传播与折射的矩阵)
    • 4.6.2 Matrix Treatment 2: Lens Matrix(矩阵处理2：透镜矩阵)
    • 4.6.3 Matrix Treatment 3: Relations between Matrix Elements and Cardinal Points(矩阵处理3：矩阵元与主点的联系)
    • 第四章习题
  • Chapter 5 Interference and Coherence(Part 1)
    • 5.0 What is Interference(什么是干涉)
    • 5.1.1 Superposition of Waves: General Case(波叠加的通式)
    • 5.1.2 Adding Wave with Same Frequency and Direction(同频同向波的叠加)
    • 5.1.3.1 Standing Wave 1 (驻波（上）)
    • 5.1.3.2 Standing Wave 2 (驻波（下）)
    • 5.1.4.1 Adding Waves with Different Frequencies 1: Beat and Group Velocity(不同频率波的叠加（上）：拍和群速度)
    • 5.1.4.2 Adding Waves with Different Frequencies 2: Continuous Frequency Spectrum(不同频率波的叠加（中）：连续的频谱)
    • 5.1.4.3 Adding Waves with Different Frequencies 3: property of Wave Packet and Reciprocal Relation(不
    • 5.2.1 Interference of Two Point Sources and Coherent Condition(两个点源的干涉和相干条件)
    • 5.2.2 Young's Double-Slits Experiment(杨氏双缝干涉实验)
    • 5.2.3 Another Treatment of Young's Interference, Paraxial and Far-field Condition(杨氏干涉的另一种处理，傍轴和远场条
    • 第五章习题（上）
    • 5.3.0 Interference by Thin Film(薄膜干涉)
    • 5.3.1 Equal Thickness Fringe(等厚干涉条纹)
    • 5.3.2 Equal Inclination Fringe(等倾干涉条纹)
    • 5.3.3 Michelson Interferometer(Michelson干涉仪)
    • 5.4.0 Multibeam Interference(多光束干涉)
    • 5.4.1.1 Derivation 1(理论推导（上）)
    • 5.4.1.2 Derivation 2(理论推导（下）)
    • 5.4.2.1 Discussion(结论与讨论)
    • 5.4.2.2 Application: F-P Interferometer(应用：F-P 干涉仪)
    • 5.5.0 Coherence Theory(相干理论)
    • 5.5.1 Spatial Coherence(空间相干性)
    • 5.5.2.1 Temporal Coherence(时间相干性)
    • 5.5.2.2 Coherent Time and Length(相干时间和相干长度)
    • 5.5.3.1 Definition of Correlation Function(关联函数定义)
    • 5.5.3.2 Correlation Function and Coherence(关联函数与相干)
    • 第五章习题（下）
  • Chapter 6(1)
    • 6.1 basic problem in diffraction(衍射的基本问题)
    • 6.2.1 Huygens-Fresnel Principle and Kirchhoff Euation(惠更斯-菲涅耳原理和基尔霍夫方程)
    • 6.2.2 Fresnel and Fraunhoffer Diffraction(菲涅耳与夫琅和费衍射)
    • 6.3.1 Fresnel Diffraction 1: Half Wavelength Plate(菲涅耳衍射1：半波带法)
    • 6.3.2 Fresnel Diffraction 2: Phasor Method(菲涅耳衍射2：旋转矢量法)
    • 6.3.3 Fresnel Diffraction 3: Opaque Disk and Babinet Principle(菲涅耳衍射3：圆屏衍射和Babinet原理)
    • 6.3.4 Fresnel Diffraction 4: Fresnel Zone Plate(an application)(菲涅耳衍射4：菲涅耳波带片（一个应用）)
    • 6.4.0 Fraunhoffer Diffraction: General Expression(夫琅和费衍射1：普遍表达形式)
    • 6.4.1.1 Single Slit Fraunhoffer Diffraction(单缝夫琅和费衍射)
    • 6.4.1.2 Characteristic of Single Slit Case(单缝衍射的特点)
    • 6.4.2 Fraunhoffer Diffraction for Rectangular Window(矩形窗口的夫琅和费衍射)
    • 6.4.3.1 Fraunhoffer Diffraction for Circular Aperture(圆孔的夫琅和费衍射)
    • 6.4.3.2 Diffraction Limit on Resolution(分辨率的衍射极限)
    • 第六章习题（上）
  • Chapter 6(2)
    • 6.5.1 Fraunhoffer Diffraction for 2-slits Case(双缝夫琅和费衍射)
    • 6.5.2.1 Multi-slits Dffraction 1: Intensity distribution(多缝衍射1：光强分布)
    • 6.5.2.2 Multi-slits Diffraction 2: Interference between Slits and Principal maxima(多缝衍射2：缝间干涉和主极大)
    • 6.5.2.3 Multi-slits Diffraction 3: Missing Order and Examples(多缝衍射3：缺级与例题)
    • 6.5.3.1 Grating Spectrometer(光栅光谱仪)
    • 6.5.3.2 Dispersion Relation of Grating Spectrometer(光栅光谱仪的色散关系)
    • 6.5.3.3 Dispersion Power and Resolution(色散能力和分辨率)
    • 6.5.3.4 Free Spectral Range(自由光谱程)
    • 第六章习题（下）
  • Chapter 7
    • 7.0 introducing Fourier expansion and transform(介绍傅里叶展开与变换)
    • 7.1.1 Fourier transform for periodic functions(周期函数的傅里叶展开)
    • 7.1.2 examples on Fourier expansion(傅里叶展开的例子)
    • 7.2.1 Fourier transform for general functions(一般函数的傅里叶变换)
    • 7.2.2 Fourier transforms of some typical functions and relation on width distribution(一些典型函数的傅里叶变换和分
    • 7.3.1 Dirac delta function(狄拉克delta函数)
    • 7.3.2 Fourier transform of the delta function(delta函数的傅里叶变换)
    • 7.4.1 properties of Fourier transform(傅里叶变换的性质)
    • 7.4.2 Fourier transform of derivatives(函数导数的傅里叶变换)
    • 7.4.3 what is convolution between functions(函数的卷积是什么)
    • 7.4.4 Fourier transform of convolution(卷积的傅里叶变换)
    • 7.5 relation between fourier transform and Fraunhoffer equation(傅里叶变换与夫琅禾费衍射之间的关系)
    • 7.6 Abbe image formation(阿贝成像原理)
    • 第七章习题
  • Chapter 8（上）
    • 8.1 what is polarization(什么是偏振)
    • 8.2.1 how to express polarization state(如何表达偏振态)
    • 8.2.2 unpolarized and partial polarized light(非偏振态和部分偏振态)
    • 8.3 linear polarizer(线偏振片)
    • 8.4.1.1 Jones vector（Jones 矢量）
    • 8.4.1.2 Transformation of Jones Vector(Jones 矢量的变换)
    • 8.4.2 Jones matrix(Jones 矩阵)
    • 第八章（上）习题
  • Chapter 8（下）
    • 8.5.1 Birefringence and a simple illustration
    • 8.5.2 Ordinary and Extraordinary light
    • 8.5.3 Typical Examples
    • 8.6.1 application 1-linear polarizer
    • 8.6.2.1 application 2-quarter wave plate
    • 8.6.2.2 application 2-change polarization state by quarter wave-plate
    • 8.6.2.3 application2-change direction of polarization by half-plate
    • 8.7.1
    • 8.7.2
    • 8.7.3
    • 8.7.4
    • 8.8.1
    • 8.8.2
    • 8.8.3
    • 第八章（下）习题
  • 期末测试
    • 期末测试

Taught by

Shuo Jiang

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